Robust variable selection and parametric component identification in varying coefficient models

ABSTRACT

In this paper, we study a novelly robust variable selection and parametric component identification simultaneously in varying coefficient models. The proposed estimator is based on spline approximation and two smoothly clipped absolute deviation (SCAD) penalties through rank regression, which is robust with respect to heavy-tailed errors or outliers in the response. Furthermore, when the tuning parameter is chosen by modified BIC criterion, we show that the proposed procedure is consistent both in variable selection and the separation of varying and constant coefficients. In addition, the estimators of varying coefficients possess the optimal convergence rate under some assumptions, and the estimators of constant coefficients have the same asymptotic distribution as their counterparts obtained when the true model is known. Simulation studies and a real data example are undertaken to assess the finite sample performance of the proposed variable selection procedure.

Keywords:

• B-spline
• Group variable selection
• Rank-based analysis
• SCAD
• Separation of varying and constant effects

Mathematics Subject Classification:

• Primary 62G05
• Secondary 62G20

Acknowledgments

The authors are very grateful to the editor, associate editor, and two anonymous referees for their detailed comments on the earlier version of the manuscript, which led to a much improved paper.

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11171361] and PhD Programs Foundation of Ministry of Education of China [grant number 20110191110033].